Statistical estimation for multiplicative cascades
نویسندگان
چکیده
منابع مشابه
On Estimation Theory for Multiplicative Cascades
The notion of multiplicative cascade was introduced into the statistical theory of turbulence by A.N. Kolmogorov as a phenomenological framework intended to accommodate the intermittency and large fluctuations observed in turbulent fluid flows. The basic idea is that energy is redistributed from larger to smaller scales via a splitting mechanism involving random multiplicative factors known as ...
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We study the well-known multiplicative log-normal cascade process in which the multiplication of Gaussian and log normally distributed random variables yields time series with intermittent bursts of activity. Due to the nonstationarity of this process and the combinatorial nature of such a formalism, its parameters have been estimated mostly by fitting the numerical approximation of the associa...
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A multiplicative cascade can be thought of as a randomization of a measure on the boundary of a tree, constructed from an iid collection of random variables attached to the tree vertices. Given an initial measure with certain regularity properties, we construct a continuous time, measure-valued process whose value at each time is a cascade of the initial one. We do this by replacing the random ...
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Positive T -martingales were developed as a general framework that extends the positive measure-valued martingales and are meant to model intermittent turbulence. We extend their scope by allowing the martingale to take complex values. We focus on martingales constructed on the interval T = [0, 1], and replace random measures by random functions. We specify a large class of such martingales, on...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2000
ISSN: 0090-5364
DOI: 10.1214/aos/1015957469